Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 9 - Section 9.2 - The Hyperbola - Exercise Set - Page 983: 61

Answer

$\frac{x^2}{1,210,000}-\frac{y^2}{5,759,600}=1$, right curve.
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Work Step by Step

Step 1. Draw a diagram as shown in the figure. Assume the midpoint between M1 and M2 to be the origin and the explosion point $E(x,y)$ is on a hyperbola with equation $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ with M1 and M2 as the foci. Step 2. We have $c=\frac{5280}{2}=2640\ ft$ and $2a=d_2-d_1=(2s)(1100 ft/s)=2200\ ft$, thus $a=1100\ ft$ and $a^2=1,210,000$ Step 3. We can find $b^2=c^2-a^2=2640^2-1100^2=5,759,600$ and the possible location of the explosion $E(x,y)$ is on the right curve of the hyperbola $\frac{x^2}{1,210,000}-\frac{y^2}{5,759,600}=1$
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